One-step methods with adaptive stability functions for the integration of differential equations

1973 ◽  
pp. 164-174 ◽  
Author(s):  
P. J. van der Houwen
Keyword(s):  
Differential Equations ◽  
Stability Functions ◽  
One Step

scholarly journals New Approximation Methods Based on Fuzzy Transform for Solving SODEs: II

2018 ◽  
Vol 1 (3) ◽  
pp. 30 ◽  
Author(s):  
Hussein ALKasasbeh ◽  
Irina Perfilieva ◽  
Muhammad Ahmad ◽  
Zainor Yahya
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Trapezoidal Rule ◽  
Approximation Methods ◽  
System Of Differential Equations ◽  
Fuzzy Transform ◽  
Fuzzy Partition ◽  
Fuzzy Approximation ◽  
One Step ◽  
Basic Functions

In this research, three approximation methods are used in the new generalized uniform fuzzy partition to solve the system of differential equations (SODEs) based on fuzzy transform (FzT). New representations of basic functions are proposed based on the new types of a uniform fuzzy partition and a subnormal generating function. The main properties of a new uniform fuzzy partition are examined. Further, the simpler form of the fuzzy transform is given alongside some of its fundamental results. New theorems and lemmas are proved. In accordance with the three conventional numerical methods: Trapezoidal rule (one step) and Adams Moulton method (two and three step modifications), new iterative methods (NIM) based on the fuzzy transform are proposed. These new fuzzy approximation methods yield more accurate results in comparison with the above-mentioned conventional methods.

scholarly journals On One-Step Method of Euler-Maruyama Type for Solution of Stochastic Differential Equations Using Varying Stepsizes

OALib ◽  
2016 ◽  
Vol 03 (01) ◽  
pp. 1-15
Author(s):  
Sunday Jacob Kayode ◽  
Akeem Adebayo Ganiyu ◽  
Adegoke Sule Ajiboye
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Step Method ◽  
One Step

Efficient higher order implicit one-step methods for integration of stiff differential equations

1980 ◽  
Vol 20 (1) ◽  
pp. 34-43 ◽  
Author(s):  
W. M. G. van Bokhoven
Keyword(s):  
Differential Equations ◽  
Higher Order ◽  
Stiff Differential Equations ◽  
One Step
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